@ProS2 If you are looking to open up specific IP ranges of Azure cognitive services you would need to lookup the list of Azure public IPs and open them up. I think for speech services you should open up these IPs on port 443 for HTTPS and check if it works. I would recommend you to go through these threads where a user with similar requirement was able to lockdown all IPs expect for the Azure speech studio.
https://video2.skills-academy.com/en-us/answers/questions/203507/audio-content-creation-access-denied-to-existing-s.html
https://video2.skills-academy.com/en-us/answers/questions/206212/how-to-lock-down-the-access-to-speech-resource-to.html
Thanks!!